A direct symbolic computation of center-controlled rogue waves to a new Painleve-integrable (3+1)-D generalized nonlinear evolution equation in plasmas

This paper proposes a new integrable generalized (3+1)-dimensional nonlinear partial differential equation. We apply the standard Painleve test to check the integrability, which shows the complete integrability of this equation. We employ symbolic computation directly to create the rogue waves using the center-controlled parameters ss and gamma. We create first-, second, and third-order rogue wave solutions via direct computation for various values of center-controlled parameters and suitable choices of different constants in the said equation. We obtain the bilinear equation in the auxiliary function f of the transformed variables. and. by using the transformation for dependent variable u. Using Hirota's direct method to create rogue waves up to the third order, we apply the generalized formula for rogue waves formulated by N-soliton. Using the symbolic system tool Mathematica, we illustrate the dynamics for the rogue wave solutions with various center-controlled parameters. We demonstrate how massive roguewaves, present in many nonlinear events, behave dominantly over tiny rogue waves. The equation investigates the development of long waves with small amplitudes traveling in plasma physics and wave motion in fluids and other weakly dispersive mediums. Scientific areas, including oceanography, fluid dynamics, dusty plasma, optical fibers, nonlinear dynamics, and numerous other nonlinear fields, show the occurrence of rogue waves in one way or another.